The Scottish giants are on the lookout for a new manager after Michael Beale was relieved of his duties last Sunday after just 10 months in charge.
The 43-year-old was sacked less than 24 hours after Rangers' disappointing 3-1 home defeat to Aberdeen in the Scottish Premiership, leaving the Gers seven points adrift of rivals and reigning champions Celtic at the top of the table.
Thirty-eight-year-old midfielder Steven Davis has been placed in interim charge while the club's hierarchy search for a long-term successor, and he suffered defeat in his first game in the dugout on Thursday - losing 2-1 in Cyprus to Aris Limassol in the Europa League group stage.
Rangers chairman John Bennett said last week that Davis "will remain in charge for as long as it takes to make the right appointment", with the Gers understood to have drawn up a shortlist of several potential successors.
Former Chelsea boss Lampard emerged as one of the leading candidates for the Rangers job earlier this week, with the 45-year-old allegedly interested in taking the reins at Ibrox.
Lampard has been out of work since his interim role in charge of Chelsea concluded at the end of last season, leaving the club after winning just one of his 11 matches in charge.
The Englishman was previously in charge of the West Londoners between July 2019 and January 2021 when he won 44 of his 84 games across all competitions.
In between his two managerial stints at Chelsea, Lampard spent just under a year as Everton manager, but he endured a difficult spell in the Toffees dugout, losing 24 of his 44 games in charge before being replaced by Sean Dyche.
A recent report from talkSPORT claims that Lampard had made Rangers' final shortlist to become their new manager after being interviewed by the club's board earlier this week.
However, Sky Sports News claims that Lampard is not under consideration by the Gers as they prepare to enter the final round of interviews for their vacancy from Monday onwards.
The report adds that the Rangers board are working through 'an evolving shortlist' that has been in place for several months which includes former defender Kevin Muscat, who is currently in charge of Japanese side Yokohama F Marinos.
Muscat, who played for Rangers between 2002 and 2003, succeeded ex-Celtic boss Ange Postecoglou - now at Tottenham Hotspur - at Yokohama F Marinos in 2021, and the 50-year-old has since won the 2022 J-League title and 2023 Japanese Super Cup, as well as boasting a 56.7% win rate.
Former Eintracht Frankfurt boss Oliver Glasner is also said to be in the running for the Ibrox hotseat, and the Daily Record claims that the 49-year-old Austrian hopes to 'muscle his way into the process'.
Glasner won the Europa League with Eintracht Frankfurt against Giovanni van Bronckhorst's Rangers in 2022, but he has been out of work since being dismissed by the Bundesliga club in June.
AZ Alkmaar's Pascal Jansen, Bodo/Glimt's Kjetil Knutsen and former Monaco manager Philippe Clement are other names who have been linked with the Rangers job, although sources in the Netherlands have suggested that a move for the former is unlikely as the Dutch side are flying high in second place in the Eredivisie.
Rangers chief executive James Bisgrove is said to have made initial contact with some candidates since the departure of Beale and he opted to miss Rangers' Europa League loss in midweek to work on the club's managerial search.
The Gers will look to return to winning ways under interim boss Davis when they travel to Paisley to face St Mirren in the Premiership on Sunday.